The strength of weak integrated information theory
Authors: Pedro A.M. Mediano, Fernando E. Rosas, Daniel Bor, Anil K. Seth, Adam B. Barrett
Journal: Trends in Cognitive Sciences (2022)

The integrated information theory of consciousness (IIT) is unprecedentedly ambitious in that it proposes a universal mathematical formula, derived from fundamental properties of conscious experience, to describe the quality and quantity of consciousness for any physical system that possesses it.IIT proponents believe it may solve the 'hard problem' of consciousness of why and how physical processes can be accompanied by subjective experience.However, in the current formulation, IIT formulae are not always well-defined and current empirical evidence does not support the level of specificity present in the theory.At the same time, available empirical evidence does support a weaker, less prescriptive version of the theory.We argue that distinguishing a 'weak' from a 'strong' flavour of IIT can provide a useful theoretical umbrella for ongoing empirical work, widening the overall appeal and applicability of the theory. The integrated information theory of consciousness (IIT) is divisive: while some believe it provides an unprecedentedly powerful approach to address the 'hard problem', others dismiss it on grounds that it is untestable. We argue that the appeal and applicability of IIT can be greatly widened if we distinguish two flavours of the theory: strong IIT, which identifies consciousness with specific properties associated with maxima of integrated information; and weak IIT, which tests pragmatic hypotheses relating aspects of consciousness to broader measures of information dynamics. We review challenges for strong IIT, explain how existing empirical findings are well explained by weak IIT without needing to commit to the entirety of strong IIT, and discuss the outlook for both flavours of IIT. The integrated information theory of consciousness (IIT) is divisive: while some believe it provides an unprecedentedly powerful approach to address the 'hard problem', others dismiss it on grounds that it is untestable. We argue that the appeal and applicability of IIT can be greatly widened if we distinguish two flavours of the theory: strong IIT, which identifies consciousness with specific properties associated with maxima of integrated information; and weak IIT, which tests pragmatic hypotheses relating aspects of consciousness to broader measures of information dynamics. We review challenges for strong IIT, explain how existing empirical findings are well explained by weak IIT without needing to commit to the entirety of strong IIT, and discuss the outlook for both flavours of IIT. Divide and conquerIIT (see Glossary) has gained considerable prominence among theories of consciousness, in large part because of its ambitious claim to specify the necessary and sufficient basis for any physical substrate of consciousness [1.Tononi G. et al.Integrated information theory: from consciousness to its physical substrate.Nat. Rev. Neurosci. 2016; 17: 450Crossref PubMed Scopus (568) Google Scholar]. The theory proposes a mathematical formula, derived by distilling the fundamentals of phenomenology into a small set of axioms, which is posited to describe the quantity and quality of the consciousness for any physical system that possesses it [1.Tononi G. et al.Integrated information theory: from consciousness to its physical substrate.Nat. Rev. Neurosci. 2016; 17: 450Crossref PubMed Scopus (568) Google Scholar,2.Oizumi M. et al.From the phenomenology to the mechanisms of consciousness: Integrated Information Theory 3.0.PLoS Computat. 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Conscious. 2021; (Published online August 30, 2021)https://doi.org/10.1093/nc/niab023Crossref Google Scholar] behave in concordance with the predictions of IIT and have found important clinical application in the assessment of conscious level in brain injury patients suffering disorders of consciousness [6.Re V.L. et al.Role of transcranial magnetic stimulation (TMS) combined with electroencephalography (EEG) in disorders of consciousness (DOC).J. Neurol. Sci. 2021; 429118507Abstract Full Text Full Text PDF Google Scholar,7.Casarotto S. et al.Stratification of unresponsive patients by an independently validated index of brain complexity.Ann. Neurol. 2016; 80: 718-729Crossref PubMed Scopus (175) Google Scholar]. However, the fundamental formula posited by IIT is intractable, except in certain 'toy' systems, and is ill-defined in some cases (including in the key application case of the human brain) [8.Barrett A.B. Mediano P.A. The Phi measure of integrated information is not well-defined for general physical systems.J. Conscious. Stud. 2019; 26: 11-20Google Scholar,9.Moon K. Exclusion and underdetermined qualia.Entropy. 2019; 21: 405Crossref Scopus (6) Google Scholar]. Thus, existing IIT-inspired measures do not provide specific tests of IIT (e.g., tests that distinguish IIT from other possible similar theories); instead, they demonstrate correlations between certain aspects of macroscopic neural activity and the level of consciousness, which have also been recognised as potentially relevant by other theoretical frameworks [10.Dehaene S. et al.Toward a computational theory of conscious processing.Curr. Opin. Neurobiol. 2014; 25: 76-84Crossref PubMed Scopus (207) Google Scholar,11.Luppi A.I. et al.A synergistic workspace for human consciousness revealed by integrated information decomposition.bioRxiv. 2020; (Published online November 26, 2020)https://doi.org/10.1101/2020.11.25.398081Google Scholar]. The combination of IIT's ambitious claims with these difficulties for testing its most specific, distinctive claims have generated considerable confusion and polarisation [12.Michel M. et al.An informal internet survey on the current state of consciousness science.Front. Psychol. 2018; 9: 2134Crossref PubMed Scopus (16) Google Scholar,13.Francken J. et al.An academic survey on theoretical foundations, common assumptions and the current state of the field of consciousness science.PsyArXiv. 2021; (Published online June 14, 2021)https://doi.org/10.31234/osf.io/8mbskGoogle Scholar], as well as criticism [14.Merker B. et al.The integrated information theory of consciousness: a case of mistaken identity.Behav. Brain Sci. 2021; 45e41PubMed Google Scholar, 15.Michel M. Lau H. On the dangers of conflating strong and weak versions of a theory of consciousness.PhiMiSci. 2020; (Published online December 30, 2021)https://doi.org/10.33735/phimisci.2020.II.54Crossref Google Scholar, 16.Doerig A. et al.The unfolding argument: why IIT and other causal structure theories cannot explain consciousness.Conscious. Cogn. 2019; 72: 49-59Crossref PubMed Scopus (44) Google Scholar]. With large international projects now underway attempting to pit IIT against competing theories of consciousness [17.Melloni L. et al.Making the hard problem of consciousness easier.Science. 2021; 372: 911-912Crossref PubMed Scopus (42) Google Scholar], it is crucial to clarify the landscape surrounding IIT so that empirical research can be better matched to theoretical claims.Here, we propose that the appeal and applicability of IIT can be widened by distinguishing between 'strong' and 'weak' flavours of the theory. Strong/weak distinctions have a long history in science, with two prominent examples being artificial intelligence [18.Searle J.R. Minds, brains, and programs.Behav. Brain Sci. 1980; 3: 417-424Crossref Scopus (2722) Google Scholar] and emergence [19.Bedau M. Downward causation and the autonomy of weak emergence.Principia. 2002; 6: 5-50Google Scholar, 20.Chalmers D.J. Strong and weak emergence.in: Davies P. Clayton P. The Re-Emergence of Emergence: The Emergentist Hypothesis From Science to Religion. Oxford University Press, 2006: 244-256Google Scholar, 21.Seth A.K. Measuring autonomy and emergence via Granger causality.Artif. Life. 2010; 16: 179-196Crossref PubMed Scopus (52) Google Scholar]. Broadly, a 'strong' perspective tends to have an ontological flavour, prescribing how things are; whereas a 'weak' perspective aims to describe a phenomenon, by explaining and simulating its properties. These distinctions are not only conceptually useful but also scientifically productive, as they enable scientists with a broader range of philosophies, objectives, and approaches to engage with the theories in question.In the context of IIT, these distinctions play out as follows (see Table 1 for an itemised view). In strong IIT, states of consciousness are identified with maxima of integrated information in any physical system. By contrast, weak IIT will test pragmatic hypotheses based on explanatory correlates [22.Seth A.K. Explanatory correlates of consciousness: theoretical and computational challenges.Cogn. Comput. 2009; 1: 50-63Crossref Scopus (86) Google Scholar] between the dynamics of information integration and certain aspects of consciousness. Strong IIT considers consciousness to be a fundamental universal physical property, such as charge or mass [23.Balduzzi D. Tononi G. Integrated information in discrete dynamical systems: motivation and theoretical framework.PLoS Comput. Biol. 2008; 4e1000091Crossref PubMed Scopus (249) Google Scholar], and assumes that a universally applicable formula for describing consciousness can in theory be obtained, with phenomenology and theoretical physics as the drivers in its construction. Weak IIT is agnostic on whether this is the case and hence can accommodate a broader range of philosophical perspectives. Moreover, hypotheses generated by weak IIT circumvent the tractability issues of the strong approach and can be directly formulated for empirically observable neurophysiological variables. In practice, strong IIT emphasises theoretical developments to inform new measures, while weak IIT focuses on applications of measures to guide theory. Together, they can foster complementary and mutually enriching research programmes.Table 1Key differences between weak and strong IITStrong IITWeak IITAddresses the 'hard problem' of consciousness [67.Chalmers D.J. Facing up to the problem of consciousness.J. Conscious. Stud. 1995; 2: 200-219Google Scholar]Addresses the 'real problem' of consciousness [68.Seth A.K. The Real Problem. Aeon, 2016Google Scholar]Claims an identity between consciousness and maximally integrated cause–effect structuresUses integrated information measures as explanatory correlates for properties of consciousnessApplies to all physical systemsApplies (so far) to neural systems onlyFocuses on theoretically fundamental, rather than practical, measuresFocuses on practical measures for real brain data Open table in a new tab After a brief overview of strong IIT and its theoretical challenges, this article outlines the principles behind weak IIT and sets out the advantages it offers over strong IIT, especially in terms of interpretation of empirical data. We conclude by describing some possible paths ahead for weak IIT, for it to best contribute to the development of consciousness science.Brief overview of strong IITStrong IIT [2.Oizumi M. et al.From the phenomenology to the mechanisms of consciousness: Integrated Information Theory 3.0.PLoS Computat. Biol. 2014; 10e1003588Crossref PubMed Scopus (499) Google Scholar] attempts to derive a universal formula for consciousness based on five fundamental properties of phenomenology, referred to as axioms [2.Oizumi M. et al.From the phenomenology to the mechanisms of consciousness: Integrated Information Theory 3.0.PLoS Computat. Biol. 2014; 10e1003588Crossref PubMed Scopus (499) Google Scholar,24.Barbosa L.S. et al.Mechanism integrated information.Entropy. 2021; 23: 362Crossref Scopus (11) Google Scholar]. (See Box 1 for a brief history of IIT.) The first property is intrinsicality, which says that experience is subjective, existing from the intrinsic perspective of the subject of experience. The second property, composition, states that experience is structured, being composed of several phenomenal distinctions that exist within it; for example, within a single experience one may distinguish a piano, a blue colour, a book, countless spatial locations, sounds, various emotions, and so on. Third, information, reflects that conscious experiences are informative, in the sense that each experience is specific and in some sense rules out other potential experiences that were a priori possible. Integration states that experience is unified, in that it cannot be subdivided into parts that are experienced separately. Finally, exclusion says that experience is definite, in that there do not exist simultaneous sets of experiences generated by overlapping physical systems. In addition there is existence, a 'zeroth axiom' that states that all substrates of consciousness must exist in physical terms. An innovative aspect of strong IIT is that it addresses the hard problem 'backwards', by proceeding from phenomenological axioms to mechanisms, as opposed to trying to go from mechanisms to consciousness.Box 1History of IITIIT grew out of the intuition that dynamical complexity, understood as coexistence of differentiation (the system having elements that are functionally and dynamically distinct) and integration (the system behaving coherently as a whole), ought to be a key feature of the neural activity associated with consciousness, since these properties are also general properties of (arguably) all conscious experiences [70.Tononi G. Edelman G.M. Consciousness and complexity.Science. 1998; 282: 1846-1851Crossref PubMed Scopus (1045) Google Scholar,71.Tononi G. et al.Complexity and coherency: integrating information in the brain.Trends Cogn. Sci. 1998; 2: 474-484Abstract Full Text Full Text PDF PubMed Scopus (491) Google Scholar]. This idea was first operationalised by the mutual information-based measure of neural complexity [72.Tononi G. et al.A measure for brain complexity: relating functional segregation and integration in the nervous system.Proc. Natl. Acad.Sci. U. S. A. 1994; 91: 5033-5037Crossref PubMed Scopus (1042) Google Scholar] and then by the first Φ measure in IIT 1.0, which was based on the number of possible states of the system and the statistical interdependencies between system components [73.Tononi G. Sporns O. Measuring information integration.BMC Neurosci. 2003; 4: 31Crossref PubMed Scopus (181) Google Scholar,74.Tononi G. An information integration theory of consciousness.BMC Neurosci. 2004; 5: 42Crossref PubMed Scopus (962) Google Scholar].The second version (IIT 2.0) introduced a new Φ measure based on the information generated by the system as it transitions from one state to the next [23.Balduzzi D. Tononi G. Integrated information in discrete dynamical systems: motivation and theoretical framework.PLoS Comput. Biol. 2008; 4e1000091Crossref PubMed Scopus (249) Google Scholar] – for the first time identifying consciousness with properties of dynamical transitions. At the same time, it emphasised the role of interelement causal connections as determinants of consciousness. Conscious contents, and the quality of consciousness, arise collectively from the informational relationships between the states of all subsets of the system [75.Balduzzi D. Tononi G. Qualia: the geometry of integrated information.PLoS Comput. Biol. 2009; 5: 1-24Crossref Scopus (146) Google Scholar], in principle describable by exploring Φ on all system subsets.The most recent version (IIT 3.0) identifies three additional properties of phenomenology (existence, composition, and exclusion), adding them to the properties of differentiation (which was reframed as information) and integration, to extend the mathematical formalism of integrated information and formulate a new measure, ΦMax [1.Tononi G. et al.Integrated information theory: from consciousness to its physical substrate.Nat. Rev. Neurosci. 2016; 17: 450Crossref PubMed Scopus (568) Google Scholar,2.Oizumi M. et al.From the phenomenology to the mechanisms of consciousness: Integrated Information Theory 3.0.PLoS Computat. Biol. 2014; 10e1003588Crossref PubMed Scopus (499) Google Scholar]. While ΦMax still provides a measure of the overall level of consciousness, the emphasis in IIT 3.0 is more on establishing a theoretical mapping between the cause–effect structure of a physical system and the structure of any conscious experience associated with it. Specifically, a system has a 'conceptual structure' that can be derived from the cause–effect relations between its elements and conscious experiences are identical to these conceptual structures. At the time of writing, IIT 4 is a work-in-progress [24.Barbosa L.S. et al.Mechanism integrated information.Entropy. 2021; 23: 362Crossref Scopus (11) Google Scholar] and contains intrinsicality as an additional 'axiom' (see main text).As stated in its main articles [2.Oizumi M. et al.From the phenomenology to the mechanisms of consciousness: Integrated Information Theory 3.0.PLoS Computat. Biol. 2014; 10e1003588Crossref PubMed Scopus (499) Google Scholar,25.Tononi G. Koch C. Consciousness: here, there and everywhere?.Philos. Trans. R. Soc. B Biol. Sci. 2015; 37020140167Crossref PubMed Scopus (335) Google Scholar], from these axioms, strong IIT posits postulates about the nature of the physical substrate of consciousness (PSC). From existence, intrinsicality, and information, a formula is constructed based on the probability of occurrence of each past and future state of the system given the current state, assuming that all states were equally likely a priori (i.e., in technical language, a 'maximum entropy' prior). Applying composition, the experience will depend on information provided by each system subset about the past and future of all subsets. And, applying integration, the experience depends on the extent to which whole subsets carry more information than nonoverlapping collections of their parts. From exclusion comes maximisations of integrated information: (i) over all discrete grainings of the system, in space, time, and the set of possible states of the system components; and (ii) over all system subsets. This process culminates in a measure of overall conscious level, ΦMax (i.e., the 'amount' of consciousness).In addition to specifying a formula for conscious level, strong IIT also studies the contents of consciousness in terms of the cause–effect structure of the physical substrate that gives rise to a maximum of integrated information (Box 1). Thus, strong IIT is a relatively comprehensive theory of consciousness, accounting for both the presence, degree, and character of conscious experiences. Importantly, though, all aspects of strong IIT rest on identifying maxima of integrated information in ways specified by the axioms and postulates.The full formula for computing ΦMax involves a considerable amount of mathematical detail [2.Oizumi M. et al.From the phenomenology to the mechanisms of consciousness: Integrated Information Theory 3.0.PLoS Computat. Biol. 2014; 10e1003588Crossref PubMed Scopus (499) Google Scholar,24.Barbosa L.S. et al.Mechanism integrated information.Entropy. 2021; 23: 362Crossref Scopus (11) Google Scholar], yet, as it currently stands, it has two major problems: it is not universally well-defined [8.Barrett A.B. Mediano P.A. The Phi measure of integrated information is not well-defined for general physical systems.J. Conscious. Stud. 2019; 26: 11-20Google Scholar,9.Moon K. Exclusion and underdetermined qualia.Entropy. 2019; 21: 405Crossref Scopus (6) Google Scholar], and there is logical inconsistency in the postulates [26.Mørch H.H. Is consciousness intrinsic?: A problem for the integrated information theory.J. Conscious. Stud. 2019; 26: 133-162Google Scholar]. Two reasons (amongst others) that it is ill-defined are: (i) the so-called maximum entropy prior it relies on does not exist for systems with long 'memory' (i.e., non-Markovian systems, such as the brain [27.Fuliński A. et al.Non-Markovian character of ionic current fluctuations in membrane channels.Phys. Rev. E. 1998; 58: 919Crossref Scopus (115) Google Scholar], in which the transition between states depends on the full past history of the system); and (ii) the maximisations involved can result in ties, which leaves the remainder of the calculation ill-defined and leads to the so-called 'underdetermined qualia problem' (while this situation may be unlikely in practice, it is still a problem for a theory aiming to describe consciousness at a fundamental level) [9.Moon K. Exclusion and underdetermined qualia.Entropy. 2019; 21: 405Crossref Scopus (6) Google Scholar,28.Krohn S. Ostwald D. Computing integrated information.Neurosci. Conscious. 2017; 2017nix017Crossref PubMed Google Scholar]. The logical inconsistency is that intrinsicality requires ΦMax to be an intrinsic property, while exclusion is extrinsic, since it requires a maximisation of ΦMax that involves comparisons with other systems [26.Mørch H.H. Is consciousness intrinsic?: A problem for the integrated information theory.J. Conscious. Stud. 2019; 26: 133-162Google Scholar]. Furthermore, due to the optimisations over coarse-grainings and system subsets, the complicated procedure to calculate ΦMax becomes intractable in systems with any reasonable degree of mechanistic complexity [28.Krohn S. Ostwald D. Computing integrated information.Neurosci. Conscious. 2017; 2017nix017Crossref PubMed Google Scholar].Despite these issues, the core of strong IIT rests on a simple and elegant idea: that consciousness is identical to properties of intrinsic integrated information in a system. It remains possible that a mathematical formulation that addresses the aforementioned problems, based on similar principles to those currently set out, could in the future be plausible [29.Kleiner J. Tull S. The mathematical structure of integrated information theory.Front. Appl. Math. Stat. 2021; 6: 74Crossref Scopus (4) Google Scholar,30.Barrett A.B. An integration of integrated information theory with fundamental physics.Front. Psychol. 2014; 5: 63Crossref PubMed Scopus (31) Google Scholar]. Work is ongoing on characterising probability distribution spaces in an intrinsic way [24.Barbosa L.S. et al.Mechanism integrated information.Entropy. 2021; 23: 362Crossref Scopus (11) Google Scholar,31.Barbosa L.S. et al.A measure for intrinsic information.Sci. Rep. 2020; 10: 1-9Crossref PubMed Scopus (9) Google Scholar]. Meanwhile, the debate continues about the veracity, consistency, and universality of the fundamental axioms [26.Mørch H.H. Is consciousness intrinsic?: A problem for the integrated information theory.J. Conscious. Stud. 2019; 26: 133-162Google Scholar,32.Bayne T. On the axiomatic foundations of the integrated information theory of consciousness.Neurosci. Conscious. 2018; 2018niy007Crossref Google Scholar].Empirical tests of strong IIT are likely to remain challenging, precisely because of its high level of ambition to identify the PSC precisely and universally. While certain aspects of the nature of the PSC posited by strong IIT can be empirically tested to some extent (e.g., by considering the difference between inactive versus inactivated neurons to discern if, as strong IIT suggests [33.Haun A. Tononi G. Why does space feel the way it does? Towards a principled account of spatial experience.Entropy. 2019; 21: 1160Crossref Scopus (49) Google Scholar], it is the brain's causal structure, beyond mere activity, that is responsible for consciousness), there is no existing experimental finding that favours the whole of strong IIT over mere components of it, or indeed over a weaker set of theoretical assumptions. Moreover, existing findings can be alternatively explained by a distinct theoretical framework, without committing to all the dramatic claims of strong IIT, namely weak IIT, to which we now turn.Weak IITThe goal of weak IIT, as outlined here, is to search for empirically measurable and powerful explanatory correlates of various aspects of consciousness. Weak IIT shares many motivations with strong IIT, but has a focus on practical measures for real brain data. In particular, weak IIT preserves the idea, central to IIT since its inception, that neural substrates of consciousness must reflect two key phenomenological observations: (i) each conscious moment is highly informative (it is one of a vast repertoire of possible experiences); and (ii) each conscious experience is integrated (it is experienced as a coherent whole) (Box 2). However, and crucially, weak IIT no longer claims an identity relationship; on weak IIT, integrated information is an explanatory correlate of consciousness, but it may not be a strictly necessary or sufficient condition for it. Accordingly, weak IIT does not commit to all the axioms of strong IIT and does not make claims of generalisation beyond the brain.Box 2Integrated experience, integrated dynamicsThe core theoretical argument behind weak IIT is that an integrated experience in the phenomenological sense should be generated by integrated brain activity in the statistical sense.The argument rests on two assumptions. The first is that, phenomenologically, conscious experience is integrated (or unified), as all elements within it form a single cohesive whole and changing any one of them would change the experience altogether [76.Bayne T. The Unity of Consciousness. Oxford University Press, 2010Crossref Scopus (116) Google Scholar]. The second is that multiple aspects of any given experience (from shapes and colours to sounds and evoked memories) are encoded by different regions in the brain. Therefore, if these brain regions are to give rise to conscious experience, they should do so through statistical interactions spanning multiple brain regions [77.Rosas F.E. et al.Quantifying high-order interdependencies via multivariate extensions of the mutual information.Phys. Rev. E. 2019; 100032305Crossref PubMed Scopus (31) Google Scholar].Similarly, weak IIT assumes that a rich conscious life is generated, in part, by the large number of different experiences available. In other words, any particular subjective experience is informative, by virtue of ruling out many other possible alternative experiences. Dynamically, this translates to the statement that the brain must have access to and spontaneously visit a large and diverse repertoire of states mapping onto those possible experiences (as opposed to strong IIT, which only requires states to be accessible in principle, not necessarily visited in practice). This property is related to the pre-IIT concept of differentiation (cf. Box 1): a system cannot visit many states if all of its parts are fully correlated, therefore, some degree of differentiation is needed for the system to be informative.Taken together, these two (brief) arguments suggest a link between consciousness and properties of neural dynamics: specifically, that the joint dynamics of brain regions must be highly diverse yet statistically interdependent.Separating weak IIT from strong IIT helps interpret a range of existing empirical work that has previously been lumped together under a single IIT banner. Broadly, any practical measure of differentiation, information, and/or integration has the potential to contribute to (or test) weak IIT. In fact, much work has already been carried out on what could be considered weak IIT, via the application of such measures to various datasets [4.Casali A.G. et al.A theoretically based index of consciousness independent of sensory processing and behavior.Sci. Transl. Med. 2013; 5198ra105Crossref PubMed Scopus (566) Google Scholar,34.Lord L.D. et al.Understanding principles of integration and segregation using whole-brain computational connectomics: implications for neuropsychiatric disorders.Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 2017; 37520160283PubMed Google Scholar, 35.Luppi A.I. et al.Consciousness-specific dynamic interactions of brain integration and functional diversity.Nat. Commun. 2019; 10: 1-12Crossref PubMed Scopus (68) Google Scholar, 36.Canales-Johnson A. et al.Dissociable neural information dynamics of perceptual integration and differentiation during bistable perception.Cereb. Cortex. 2020; 30: 4563-4580Crossref PubMed Scopus (13) Google Scholar]. Previously, many of these studies have been described as providing support for strong IIT; however, weak IIT offers a more parsimonious interpretation, since not all the axioms and postulates of strong IIT are needed to account for the results. Moreover, given the concerns raised over ΦMax [8.Barrett A.B. Mediano P.A. The Phi measure of integrated information is not well-defined for general physical systems.J. Conscious. Stud. 2019; 26: 11-20Google Scholar,9.Moon K. Exclusion and underdetermined qualia.Entropy. 2019; 21: 405Crossref Scopus (6) Google Scholar,26.Mørch H.H. Is consciousness intrinsic?: A problem for the integrated information theory.J. Conscious. Stud. 2019; 26: 133-162Google Scholar], it is problematic to consider Φ-like measures designed for experimental application as actually testing an approximation to strong IIT, beyond testing weak IIT.Weak IIT allows researchers to work on developing and experimentally testing the core intuitions of IIT without committing to the more contentious claims central to strong IIT (especially its identity claim) and/or having to address the open mathematical problems with ΦMax. Importantly, there